# Neural Likelihood Approximation for Integer Valued Time Series Data

arXiv: https://arxiv.org/abs/2310.12544 · HTML: https://mlsanity.com/paper/2310.12544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 60 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 18 of 18)

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- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Lookahead Strategies for Sequential Monte Carlo](https://mlsanity.com/paper/1302.5206/) (2013)
- [Direct statistical inference for finite Markov jump processes via the matrix exponential](https://mlsanity.com/paper/1809.07110/) (2018)

## Abstract (arXiv)

Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations cannot be ignored and stochastic effects are important. The inference of the parameters of such models, from time series data, is challenging due to intractability of the likelihood. To work at all, current simulation based inference methods require the generation of realisations of the model conditional on the data, which can be both tricky to implement and computationally expensive. In this paper we instead construct a neural likelihood approximation that can be trained using unconditional simulation of the underlying model, which is much simpler. We demonstrate our method by performing inference on a number of ecological and epidemiological models, showing that we can accurately approximate the true posterior while achieving significant computational speed ups compared to current best methods.